Regarding income inequality:
Economists used to rely on household surveys in which individuals (or households) reported their earnings, social benefits, etc. Although this is still done, recent studies rely more and more on the income data recorded in the tax files due to its larger coverage and accuracy (especially at the top of the distribution).
You can find the most complete historic series of income (& wealth) inequality based on tax records in the World Wealth and Income Inequality Database:
Other sources to compare income inquality and poverty levels across countries and time are:
- The World Bank: https://data.worldbank.org/
- The UNU-WIDER World Income Inequality Database: https://www.wider.unu.edu/project/wiid-world-income-inequality-database
- The Standardized World Income Inequality Database
- Branko Milanovic's data of Gini coefficients in 1950-2022 for 170 countries: http://econ.worldbank.org/WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/0,,contentMDK:22301380~pagePK:64214825~piPK:64214943~theSitePK:469382,00.html
For nice visualizations over time you can see Gap Minder:
Regarding intergenerational income mobility (~social mobility):
The first studies of intergenerational income mobility (i.e. how income levels compare across several generations) relied on household surveys in which retrospective information about parents' income was collected. Then, panel surveys started to be used when they had a sufficient coverage (panel surveys follow the same individuals -and often their children- over time).
Some examples of long-panels available are:
- PSID for the US (1968-Today): https://psidonline.isr.umich.edu/
- BCS for the UK (1970-Today): https://bcs70.info/
- BHPS for the UK (1991-Today): https://www.iser.essex.ac.uk/bhps
- SOEP for Germany (1984-Today): https://www.diw.de/en/soep
In the last decades some studies of intergenerational mobility have also used income data coming from tax records, linking the files of parents' and their children (see the pioneering work of Miles Corak (1999) for Canada). That is the kind of data that Chetty and coauthors have used.
Gregory Clark and coauthors have been relying on rare surnames and their over-representation in top institutions (e.g. Cambridge and Oxford) to track social mobility over centuries. You can check this work in his website.
Just mentioning that there are works looking at intergenerational mobility of other dimensions besides income, such as wealth (e.g. Clark and Cummins, 2015), educational attainment (e.g. Lindhal et al., 2015), or even attitudes (Dohmen et al., 2011).